The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9.

Question:

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.

Solution:

Let the measures of the angles of the given quadrilateral be $(3 x)^{\circ},(5 x)^{\circ},(7 x)^{\circ}$ and $(9 x)^{\circ}$.

Sum of all the angles of a quadrilateral is $360^{\circ}$.

$\therefore 3 x+5 x+7 x+9 x=360$

$24 x=360$

$x=15$

Angles measure:

$(3 \times 15)^{\circ}=45^{\circ}$

$(5 \times 15)^{\circ}=75^{\circ}$

$(7 \times 15)^{\circ}=105^{\circ}$

$(9 \times 15)^{\circ}=135^{\circ}$

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